( 654 ) 



volume. Then both the point of detachment and the point of contraction 

 fall in the ''figure. 



The consequences for the change of the r,.r-projection of the binodal 

 curve with variation of temperature will probably be clear from the 

 figures 3 — 5 without further elucidation in these three cases. With regard 

 to the frequency with which the three cases occur, it is evident that 

 the last case will occur only rarely, with exceptionally high values of 



db da , _ /d/A . 



— and , or in general of I ^- I. 11ns case would be altogether 



dx dx \Q>v) 



impossible, if we had to take the temperature of the triple point, 



and the volume which the saturated vapour then has, into account, 



for this amounts certainly to some thousands of times b, and hence 



there will probably never be any question of an intersection of 



JV = with the branch D = holding for the large volumes at 



the triple point temperature. But for our case we have not to reckon 



with this temperature, but with the highest temperature at which the 



binodal curve solid-fluid has still three points in common with the axis 



.i' = 0, and this is evidently the temperature of point A in fig. 1. 



This, now, can probably lie very considerably above the triple point, 



and moreover — as we observed before — not the volume of the 



saturated vapour, but the much smaller one of the maximum of the 



isotherm must be introduced here. If we e. g. put the temperature 



of A so high that the maximum point of the isotherm lies at 



a volume 46, the expression will already become positive with 



— = 3b 1 , or b i = 4:b l and v s near b, (da/ dx is negative). So the 

 dx 



case of 3 is, indeed, possible, but it also appears thai it will occur 



only in exceptional cases *). 



With none of these three cases do the T, x- and p, .r-figures construed 



by van der Waals and Smits, agree. They agree in so far with that 



mentioned under 3, that the point of detachment and the point of 



contraction are assumed to fall within the figure. But it is at the 



same time clear from the tu'-ligures, that a complication must begin 



') ft appears from what has been said here that the figures 6—9 are meant 

 quite schematically, for though we have drawn several binodals solid-fluid which 

 hold for different temperatures, we have left the loci iV = and Z) = unchanged. 

 This has, of course, been done to save space, for else we could not have repre- 

 sented much more than one temperature in each figure without rendering the 

 figures indistinct. But after what has been said it is clear that also the points 

 Q and Q' move, and that it might e.g. very well happen that at lower tempera- 

 tures the point Q' is not yet present in the figure, and that it makes its appearance 

 only at higher temperatures. The following figures, too, are meant schematically, 

 and serve only to elucidate the properties mentioned in the text. 



